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- Mathematics Stack Exchange
Q A for people studying math at any level and professionals in related fields
- Calculate the cohomology group of $U(n)$ by spectral sequence.
Your method seems like the correct one Have you tried working through the spectral sequence for some small n?
- Prove that the sequence (1+1 n)^n is convergent [duplicate]
I know the proof using binomial expansion and then by monotone convergence theorem But i want to collect some other proofs without using the binomial expansion *if you could provide the answer w
- geometry - Circle revolutions rolling around another circle . . .
At the risk of sounding very un-mathematical, how do the (infinite set of) points on the circumference of each circle map to each other to accomplish this? Consider Circle A rolling along a straight line the length of the circumference of Circle B Then it will revolve 3 times
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- $U (n)$ is a compact group. Proof. - Mathematics Stack Exchange
$U (n)$ is the preimage of the unit circle under the determinant map, and thus closed
- When is the group of units in $\\mathbb{Z}_n$ cyclic?
@Lhf The question is certainly not a duplicate of the linked question, since the author is asking additionally a more general question, namely "What are those number theoretic situations?" (where the unit group is cyclic) This is an interesting question that is not addressed at all in the proposed duplicate
- For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
17 Un U n is cyclic iff n n is 2 2, 4 4, pk p k, or 2pk 2 p k, where p p is an odd prime The proof follows from the Chinese Remainder Theorem for rings and the fact that Cm ×Cn C m × C n is cyclic iff (m,n)= 1 (m, n) = 1 (here Cn C n is the cyclic group of order n n)
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